 | John Playfair - Euclid's Elements - 1833 - 346 pages
...Therefore any two sides, &c. QED PROP. XXI. THEOR. If from the ends of one side of a triangle, tJiere be drawn two straight lines to a point within the triangle, these two lines shall he less than the other two sides of the triangle, but shall contain a greater angle.... | |
 | Euclid - 1835 - 540 pages
...of a triangle there be See N. drawn two straight lines to a point within the triangle, these sJiall be less than the other two sides of the triangle,...two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC to the point D within it ; BD and DC are less than the other... | |
 | John Playfair - Geometry - 1836 - 148 pages
...impossible ; and, therefore, ACB is not a right angle. Therefore, From, &c. QED PROP. XII. THEOR. If from the ends of the side of a triangle there be drawn...be less than the other two sides of the triangle. Let the two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC,... | |
 | Mathematics - 1836 - 488 pages
...Any two sides of a triangle are together greater than the third side. XXI. If from the ends of one side of a triangle, there be drawn two straight lines to a point within the triangle, these two lines shall be less than the other two sides of the triangle, but shall contain a greater angle.... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...point within the triangle, these two lines shall be less than the other two sides of the triangle, biit shall contain a greater angle. Let the two straight lines BD, CD be drawn from B, <I, the ends of the side BC of the triangle ABC, to the point D within it ; BD and DC are less than... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...that similarly each of the other pairs of sides is > the remaining side. PROPOSITION XXI. Theorem. If from the ends of the side of a triangle there be drawn...of the triangle, but shall contain a greater angle. • Steps of the Demonstration. 1. Prove that BA + AC > BE + EC, 2. that BE + EC > CD + DB, 3. that... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...that the sides AB, BC, are greater than CA, and BC, CA, greater than AB. PROPOSITION XXI. THEOREM. If from the ends of the side of a triangle, there be...straight lines to a point within the triangle, these two lines shall he less than the other two sides of the triangle, but shall contain a greater angle.... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...than CA, and BC, CA greater than AB. SCHOLIUM. 23 E PROP. XXI. THEOR. If from, the ends of one si'le of a triangle, there be drawn two straight lines to a point within the triangle, these two lines shall be less than the other two sides of the triangle, but shall contain a greater angle.... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...greater than CA, and BC, CA greater than AB. Therefore any two sides, &c. Q,. ED PROP. XXI. THEOR. IF, from the ends of the side of a triangle, there be...two straight lines BD, CD be drawn from B, C, the ends of the side BC of the triangle ABC, to the point D within it ; BD and DC are less than the other... | |
 | Euclides - 1838 - 264 pages
...than the third Mr.." and reason as follows: " For, since BA and AC are together PROP. XXI. THEOR. If from the ends of the side of a triangle there be drawn...to a point within the triangle, these shall be less man the other two sides of the triangle, but shall contain a greater angle. Let ABC be a triangle,... | |
| |
If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let... 
